"He's not the first to leave Kolkata," says novelist Amit Chaudhuri, "and he won't be the last. People have been leaving this city for more than 30 years."

He pauses to reflect on the sad decline of the City of Joy, the former Calcutta, the capital of India until 1911 and once the pride of the British empire. "They began to leave at about the same time as industry began to leave, in the late 1960s," he says.

Azim flew back into Kolkata last week after his visa ran out and his £15,000-a- year salary proved insufficient for him to secure a new one. But rather than expressing anger at his treatment, he surprised many by saying that he wanted to return to Britain.

"I am not surprised that he wants to go back to the UK," says Chaudhuri. "Badar is from a less privileged background, and from a minority [he is a Muslim]. Anyone might feel that opportunities are greater elsewhere."

Badar Azim's family live high up in an apartment block reached along narrow lanes lined with tiny workshops in which young men – some of them very young indeed – work for long hours making leather goods, mainly shoes. It is a hard life.

The oldest of three brothers – his father is a welder earning 3,000 rupees (£32) a month; his mother describes herself as a housewife – the young Badar shared a bed with his brothers in the family's single room in this building in a poor part of the city. Their parents slept on the floor.

However, the couple knew the value of education and scrimped and saved to put the boys through school, helped by a charitable organisation. Badar went on to study for a degree in the UK before securing the Buckingham Palace job. It was an irresistible story.

Last week a media circus assembled in the street outside the Azims' home, a street that already resembled a scene out of a Dickens television adaptation, complete with a large man knuckling his way through the throng, a heavily bandaged woman being pushed on a cart, other women washing clothes in front of their homes, a small child hammering away at a pair of shoes and another lugging a large bag of water bottles through the crowd.

Neither the family nor their neighbours appreciated the attention, nor the focus on the way they live. According to Chaudhuri, that is because there exists a greater sense of dignity among Kolkata's poor than in other parts of the country.

"In this city," he said, "less privileged people have more of a sense of their own dignity than one might expect. It may or may not be justified by their worldly possessions, income or education but, at least on some level, working people did develop a more dignified sense of themselves during the time of the Left Front government."

The city, built on the banks of the Hooghly river, remains the capital of West Bengal and one survey last year placed it third behind Delhi and Mumbai as India's most attractive city. It has a fine metro system, some lovely old architecture and a rich cultural history. It is close to important markets such as those of China and south-east Asia in a state that is rich in minerals. It should be thriving, yet it is not. Despite a glut of new buildings, it has stagnated.

The population stands at just over 5 million, barely 500,000 more than in 1950. While rival cities have surged ahead, the last census, in 2011, showed that Kolkata's population had fallen by 86,197, while the city's share of India's industrial output had dropped from a quarter in 1950 to just 7% at the turn of this century.

"There was a time, during the 1960s, when Calcutta had it all, but because Bengalis by nature like to argue and to be activists, there was a lot of turmoil here and that has made it a very unfriendly place for corporates," says Nandan Bagchi, 60, a prominent figure in the city's cultural scene.

Dipankar Dasgupta, professor of economics at the Indian Statistical Institute in Kolkata, says that good business leaders and investors found it difficult to survive here under the communists: "The few that remained were concentrating on real estate, but that is not an industry you want to depend on for the growth of a state. People who were any good did not see much of a future here."

The city faces a paradox, he says. Land that could be used for factories is owned by thousands of small farmers, and striking individual deals is almost impossible. But the government will not intervene because it needs rural votes.

"You have to keep the farmers happy to stay in power. To keep them happy you cannot interfere in land acquisition. You have to leave it to the markets, but it does not work. It all looks hunky dory, but who is going to come here?"

This is the question taxing the new Trinamool Congress government, led by chief minister Mamata Banerjee. It was Banerjee who, while still in opposition, helped thwart plans by the Tata company to build a factory in the state to make its new small and fuel-efficient Nano car. The combative politician sided with the farmers, who were complaining that they would lose their land. In the end Tata gave up and built the factory in the thriving state of Gujarat.

Last week Banerjee was in Mumbai, attempting to persuade investors there to plough money into her own state. But a previous trip she made to Delhi in December fell flat.

Bagchi, who is a musician and writer, laments the lack of opportunities this means for bright young men like 25-year-old Badar. "A lot of my friends," he says, "left because of lack of opportunity, but they miss the city because of the human values. Nobody cared what you earned or did for a living as long as you were acceptable as a human being. People miss the mellowness."

Yet Kolkata now faces the same challenges as other Indian cities, without many of their advantages.

"We have had growth in the past few years, but it has been accompanied by unbelievable income inequality," says Dasgupta. "Come out on to the street and you have these little children following you begging for coins and working in the informal sector where there are absolutely no rules. These are the people who form the majority. People are interested in investing in the market serving the top 10%, but the rest are living in darkness."